If P=NP, then NP = coNP. Why is this so?

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I read that if we assume that P = NP, then NP = coNP. I am unable to understand why this is so.

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It is easy to show that $P=coP$ (think about it). Now, if $P=NP$ then $coP=coNP$, so that $NP=P=coP=coNP$.